Numerical Linear Algebra And Applications

Author : Biswa Nath Datta
Publisher : SIAM
Page : 546 pages
File Size : 40,7 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780898717655

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Numerical Linear Algebra and Applications by Biswa Nath Datta Pdf

Full of features and applications, this acclaimed textbook for upper undergraduate level and graduate level students includes all the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems. Drawing from numerous disciplines of science and engineering, the author covers a variety of motivating applications. When a physical problem is posed, the scientific and engineering significance of the solution is clearly stated. Each chapter contains a summary of the important concepts developed in that chapter, suggestions for further reading, and numerous exercises, both theoretical and MATLAB and MATCOM based. The author also provides a list of key words for quick reference. The MATLAB toolkit available online, 'MATCOM', contains implementations of the major algorithms in the book and will enable students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy.

Author : Larisa Beilina,Evgenii Karchevskii,Mikhail Karchevskii
Publisher : Springer
Page : 450 pages
File Size : 53,6 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9783319573045

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Numerical Linear Algebra: Theory and Applications by Larisa Beilina,Evgenii Karchevskii,Mikhail Karchevskii Pdf

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigenproblems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

Author : William Ford
Publisher : Academic Press
Page : 629 pages
File Size : 40,5 Mb
Release : 2014-09-14
Category : Mathematics
ISBN : 9780123947840

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Numerical Linear Algebra with Applications by William Ford Pdf

Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra Detailed explanations and examples A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra Examples from engineering and science applications

Author : James E. Gentle
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206231

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Numerical Linear Algebra for Applications in Statistics by James E. Gentle Pdf

Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.

Author : James W. Demmel
Publisher : SIAM
Page : 426 pages
File Size : 47,7 Mb
Release : 1997-08-01
Category : Mathematics
ISBN : 9780898713893

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Applied Numerical Linear Algebra by James W. Demmel Pdf

This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Author : James E. Gentle
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 40,6 Mb
Release : 2007-07-27
Category : Computers
ISBN : 9780387708720

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Matrix Algebra by James E. Gentle Pdf

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Author : William Layton,Myron Mike Sussman
Publisher : World Scientific
Page : 274 pages
File Size : 44,9 Mb
Release : 2020-07-14
Category : Mathematics
ISBN : 9789811223914

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Numerical Linear Algebra by William Layton,Myron Mike Sussman Pdf

'The numerical algorithms presented are written in pseudocode and based on MATLAB, a programming and numeric computing platform widely used in STEM fields. Thus, no formal training in computer science or knowledge of any specific programming language is needed to parse the algorithms. Summing up: Recommended.'CHOICEMany students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Each topic is presented as algorithmic ideas and through a foundation based on mostly applied analysis. By picking a path through the book appropriate for the level, it has been used for both senior level undergraduates and beginning graduate classes with students from diverse fields and backgrounds.

Author : Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas
Publisher : Cambridge University Press
Page : 456 pages
File Size : 45,9 Mb
Release : 1989-08-25
Category : Computers
ISBN : 0521339847

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Introduction to Numerical Linear Algebra and Optimisation by Philippe G. Ciarlet,Bernadette Miara,Jean-Marie Thomas Pdf

The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector spaces, advanced calculus, and some elementary notations from functional analysis. The book is in two parts. The first deals with numerical linear algebra (review of matrix theory, direct and iterative methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimisation (general algorithms, linear and nonlinear programming). The author has based the book on courses taught for advanced undergraduate and beginning graduate students and the result is a well-organised and lucid exposition. Summaries of basic mathematics are provided, proofs of theorems are complete yet kept as simple as possible, and applications from physics and mechanics are discussed. Professor Ciarlet has also helpfully provided over 40 line diagrams, a great many applications, and a useful guide to further reading. This excellent textbook, which is translated and revised from the very successful French edition, will be of great value to students of numerical analysis, applied mathematics and engineering.

Author : Biswa Nath Datta
Publisher : Unknown
Page : 680 pages
File Size : 48,7 Mb
Release : 2008
Category : Algebras, Linear
ISBN : 0759322546

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Numerical Linear Algebra and Applications by Biswa Nath Datta Pdf

Author : Grégoire Allaire,Sidi Mahmoud Kaber
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 42,6 Mb
Release : 2008-12-17
Category : Mathematics
ISBN : 9780387689180

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Numerical Linear Algebra by Grégoire Allaire,Sidi Mahmoud Kaber Pdf

This book distinguishes itself from the many other textbooks on the topic of linear algebra by including mathematical and computational chapters along with examples and exercises with Matlab. In recent years, the use of computers in many areas of engineering and science has made it essential for students to get training in numerical methods and computer programming. Here, the authors use both Matlab and SciLab software as well as covering core standard material. It is intended for libraries; scientists and researchers; pharmaceutical industry.

Author : Tom Lyche
Publisher : Springer Nature
Page : 376 pages
File Size : 45,8 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9783030364687

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Numerical Linear Algebra and Matrix Factorizations by Tom Lyche Pdf

After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.

Author : S.K. Godunov,A.G. Antonov,O.P. Kiriljuk,V.I. Kostin
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 53,7 Mb
Release : 1993-06-30
Category : Computers
ISBN : 0792323521

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Guaranteed Accuracy in Numerical Linear Algebra by S.K. Godunov,A.G. Antonov,O.P. Kiriljuk,V.I. Kostin Pdf

There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interest ing problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solv ing linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of com lead putations is guaranteed. As far as the final program product is con cerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where abso lutely all errors of input data and machine round-offs are taken into account. 2.

Author : Xiao-Qing Jin
Publisher : Unknown
Page : 188 pages
File Size : 43,7 Mb
Release : 2015
Category : Algebras, Linear
ISBN : 7030464257

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Numerical Linear Algebra and Its Applications by Xiao-Qing Jin Pdf

Author : Philip E. Gill,Walter Murray,Margaret H. Wright
Publisher : Westview Press
Page : 454 pages
File Size : 41,8 Mb
Release : 1991-07-22
Category : Mathematics
ISBN : UOM:39015018919905

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Numerical Linear Algebra And Optimization by Philip E. Gill,Walter Murray,Margaret H. Wright Pdf

Numerical linear algebra and opt./Gill, P.E.- v.1

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 53,7 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.